The involute

The involute is defined as the path of a point on a straight line which rolls without slip along the circumference of a cylinder. The involute curve will be required in a later chapter for the construction of gear teeth.

Involute construction

1 Draw the given base circle and divide it into, say, 12 equal divisions as shown in Fig. 10.8. Generally only the first part of the involute is required, so the given diagram shows a method using half of the length of the circumference.

3 From point 6, mark off a length equal to half the length of the circumference.

4 Divide line 6G into six equal parts.

5 From point 1, mark point B such that 1B is equal to one part of line 6G.

6 From point 2, mark point C such that 2C is equal to two parts of line 6G.

Repeat the above procedure from points 3, 4 and 5, increasing the lengths along the tangents as before by one part of line 6G.

7 Join points A to G, to give the required involute.

Alternative method

1 As above, draw the given base circle, divide into, say, 12 equal divisions, and draw the tangents from points 1 to 6.

2 From point 1 and with radius equal to the chordal length from point 1 to point A, draw an arc

Engineering Drawing Involute

terminating at the tangent from point 1 at point B.

3 Repeat the above procedure from point 2 with radius 2B terminating at point C.

4 Repeat the above instructions to obtain points D, E, F and G, and join points A to G to give the required involute.

The alternative method given is an approximate method, but is reasonably accurate provided that the arc length is short; the difference in length between the arc and the chord introduces only a minimal error.

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